The Universal Turing Machine A Half-Century Survey / Edition 2

"On Computable Numbers, with an Application to the Entscheidungsproblem”, Alan Turing’s paper of 1937, contained his thesis that every effective computation can be programmed on such an automation as that called Turing machine. Furthermore it proved the unsolvability of the halting problem and of the decision problem for first order logic, and it presented

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"On Computable Numbers, with an Application to the Entscheidungsproblem”, Alan Turing’s paper of 1937, contained his thesis that every effective computation can be programmed on such an automation as that called Turing machine. Furthermore it proved the unsolvability of the halting problem and of the decision problem for first order logic, and it presented the invention of the universal Turing machine. It is that publication that will presumably be acknowledged as marking sub specie aeternitatis the beginning of the "computer age”.This volume recognizes the still continuing influence of the Turing machine concept by collecting contributions from international specialists in logic, computability, mathematics, biology, physics, linguistics, and cognitive science, thus signalling the exceptionally wide scope of that concept.

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Table of Contents

I.- Alan Turing and the Turing Machine.- Turing’s Analysis of Computability, and Major Applications of It.- The Confluence of Ideas in 1936.- Turing in the Land of O(z).- Mathematical Logic and the Origin of Modern Computing.- II.- From Universal Turing Machines to Self-Reproduction.- Computerizing Mathematics: Logic and Computation.- Logical Depth and Physical Complexity.- The Busy Beaver Game and the Meaning of Life.- An Algebraic Equation for the Halting Probability.- The Price of Programmability.- Gandy’s Principles for Mechanisms as a Model of Parallel Computation.- Influences of Mathematical Logic on Computer Science.- Language and Computations.- Finite Physics.- Randomness, Interactive Proofs, and Zero-Knowledge — A Survey.- Algorithms in the World of Bounded Resources.- Beyond the Turing Machine.- Structure.- Mental Images and the Architecture of Concepts.- The Fifth Generation’s Unbridged Gap.- On the Physics and Mathematics of Thought.- Effective Processes and Natural Law.- Turing Naturalized: Von Neumann’s Unfinished Project.- Complexity Theory and Interaction.- Mechanisms for Computing Over Arbitrary Structures.- Comparing the Church and Turing Approaches: Two Prophetical Messages.- Form and Content in Thinking Turing Machines.